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The set S of numbers has the following properties

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The set S of numbers has the following properties [#permalink] New post 16 Oct 2005, 10:57
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A
B
C
D
E

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16) The set S of numbers has the following properties:
I) If x is in S, then 1/x is in S.
II) If both x and y are in S, then so is x + y.
Is 3 in S?
(1) 1/3 is in S.
(2) 1 is in S.


I have the ans as A...but its nt the right one. Ok just to let u know the ans here is D...and I dont understand how can B qualify. This question is from the forum itself & the logic is that nothing in property II prevents from having the same number.

when x & y are 2 diff variables....how can we assume as it being one number??? does this rule really apply to all DS or GMAt questions.
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 [#permalink] New post 16 Oct 2005, 11:01
Ok. The stem doesn't say that the numbers in the set are unique.

We know 1 is in S. X=1
So, Y = 1/X is also in S, => Y=1/1 = 1
Since X+Y is also in S, X+Y = 1 + 1 = 2 is in S.

So, now we know 2 and 1 are in S. Consider this new x and y. This means x+y should be in S = 1+2 = 3

Hence, B is also sufficient.
  [#permalink] 16 Oct 2005, 11:01
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The set S of numbers has the following properties

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